Practice Construction Of The Equivalence Relation (22.4.2.1)

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6 sample questions

Question 1.
What is a partition of a set?
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Think of how a pizza can be cut into slices.
Question 2.
Does a partition of a set have overlapping subsets?
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Consider how two different states cannot overlap.
3Question 3.
What is an equivalence relation?
- A relation that is only symmetric.
- A relation that is reflexive
- symmetric
- and transitive.
- A relation that does not require any properties.
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Recall the properties we discussed.
4Question 4.
True or False: A partition can have overlapping subsets.
- True
- False
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Think of how subsets cannot share elements.
Question 5.
Construct a partition of the set {1, 2, 3, 4, 5} into subsets of size two.
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Think about how you can pair up elements.
Question 6.
Prove that the equivalence classes of an equivalence relation form a partition.
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Use the properties of equivalence relations in your proof.

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